Integral of Composition Functions

[kuskus94]

Homework Statement

http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc6/282312_368248176595083_1229435302_n.jpg

Homework Equations

To subtitute x into U, but that did not work.

The Attempt at a Solution

I have tried subtituting x into U like this :

http://sphotos-g.ak.fbcdn.net/hphotos-ak-snc7/578486_368249266594974_1874868606_n.jpg

The last two lines are my "goofing around" answer.

 

[clamtrox]

If you change variables, you have to change them all! You can't just leave some x's laying around. Now you have x=x(u) and you don't know how this integrates.

There is kind of a standard trick for any integral that looks like this, which is to first complete the square. What you want to do is to write the integrand into a form
$$\frac{dx}{\sqrt{A^2 - (B+Cx)^2}}$$
and then do a trigonometric substitution $B+Cx = A \sin t$